A note on mean convex 𝜆-surfaces in ℝ³

Guang, Qiang

doi:10.1090/proc/15297

A note on mean convex $\lambda$-surfaces in $\mathbb {R}^3$
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Proc. Amer. Math. Soc. 149 (2021), 1259-1266 Request permission

Abstract:

Inspired by the work of Spruck and Xiao on mean convex translators, in this note, we show that any closed and mean convex $\lambda$-surface in $\mathbb {R}^3$ with $\lambda \leq 0$ must be convex. We also give a curvature estimate for mean convex $\lambda$-surfaces in $\mathbb {R}^3$.

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